Chapter 17.3, Problem 33E

Evaluating line integrals Evaluate the line integral ò_C▿φ•dr for the following functions φ and oriented curves C in two ways.

a.    Use a parametric description of C to evaluate the integral directly.

b.    Use the Fundamental Theorem for line integrals.

31.    φ(x, y, z) = (x² + y² + z²)/2; C: r(t) = 〈cos t, sin t, t/π〉, for 0 ≤ t ≤ 2π